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The image you've uploaded shows a multiple-choice question involving the simplification of an algebraic expression. The expression provided in the image is:

\[
(5x^4 + 6x^3 + 4) + (6x^3 + 4)
\]

To simplify this, we combine like terms:

- \(5x^4\) stays as is since there is no other \(x^4\) term.
- \(6x^3 + 6x^3 = 12x^3\)
- \(4 + 4 = 8\)

Therefore, the simplified expression is:

\[
5x^4 + 12x^3 + 8
\]

Checking against the answer choices:

1. \(30x^5 + 36x^4 + 24x^3 + 16\)
2. \(30x^5 + 36x^4 + 24x^3 + 20x^2 + 16\)
3. \(30x^5 + 36x^4 + 24x^3 + 20x^2 + 24x + 16\)
4. \(16\)
5. \(36x^4 + 24x^3 + 20x^2 + 24x + 16\)
6. None

None of the provided choices match \(5x^4 + 12x^3 + 8\). Therefore, the correct answer is "None".

Would you like to understand more about how to combine like terms or any other questions? Here are some follow-up topics you might find interesting:

1. What happens if the powers of \(x\) are different across terms?
2. How would you factorize a polynomial?
3. What are the different ways to simplify complex expressions?
4. How do operations like addition and multiplication affect polynomial terms?
5. What is the importance of simplifying expressions in algebra?

**Tip**: Always recheck your work when simplifying algebraic expressions to avoid small errors, especially in exams where multiple choices may look similar.

Learn how to simplify the polynomial expression (5x^2 + 6x + 4) × (6x^3 + 4) using the distributive property. Detailed step-by-step explanation provided, suitable for students in Grades 9-12.

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